Computational invariant theory

268 pages, parution le 17/06/2002

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Résumé

Throughout the history of invariant theory, computational methods have always been at the center of attention. This book, the first volume of the new subseries on "Invariant Theory and Algebraic Transformation Groups", provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Special features are an introductory chapter on Gröbner basis methods and a chapter on applications, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. Both authors have made significant contributions to the theory and practice of algorithmic invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.
The book will be very useful to postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory.

Table of contents

Constructive ideal theory
Invariant theory
Invariant theory of finite groups
Invariant theory of reductive groups
Applications of invariant theory
Linear algebraic groups